A die is rolled 24 times. Use the Central Limit Theorem to estimate the probability that the sum is greater than 84.

• 0.4
• 0.45
• 0.5
• 0.55
• 0.6

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

Solution: C

On each roll, the expected number is

[[math]] 1/6 \sum_{i=1}^6 i = 3.5 [[/math]]

Hence the expected sum for 24 rolls is 84. By the central limit theorem, the probability that 24 rolls exceed 84 is 1/2.